# Chapter 9

```CHAPTER 9: PHASE DIAGRAMS
• When we combine two elements...
what equilibrium state do we get?
• In particular, if we specify...
--a composition (e.g., wt%Cu - wt%Ni), and
--a temperature (T)
then...
How many phases do we get?
What is the composition of each phase?
How much of each phase do we get?
Chapter 9- 1
THE SOLUBILITY LIMIT
• Solubility Limit:
Max concentration for
which only a solution
occurs.
• Ex: Phase Diagram:
Water-Sugar System
Question: What is the
solubility limit at 20C?
If Co &lt; 65wt% sugar: sugar
If Co &gt; 65wt% sugar: syrup + sugar.
Callister 6e.
• Solubility limit increases with T:
e.g., if T = 100C, solubility limit = 80wt% sugar.
Chapter 9- 2
COMPONENTS AND PHASES
• Components:
The elements or compounds which are mixed initially
(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regions
that result (e.g., a and b).
AluminumCopper
Alloy
Fig. 9.0,
Callister 3e.
Chapter 9- 3
EFFECT OF T &amp; COMPOSITION (Co)
• Changing T can change # of phases: path A to B.
• Changing Co can change # of phases: path B to D.
• watersugar
system
Fig. 9.1,
Callister 6e.
Chapter 9- 4
PHASE DIAGRAMS
• Tell us about phases as function of T, Co, P.
• For this course:
--binary systems: just 2 components.
--independent variables: T and Co (P = 1atm is always used).
• Phase
Diagram
for Cu-Ni
system
Adapted from Fig. 9.2(a), Callister 6e.
(Fig. 9.2(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P.
Nash (Ed.), ASM International,
Materials Park, OH (1991).
Chapter 9- 5
PHASE DIAGRAMS: # and types of phases
• Rule 1: If we know T and Co, then we know:
--the # and types of phases present.
• Examples:
Cu-Ni
phase
diagram
Adapted from Fig. 9.2(a), Callister 6e.
(Fig. 9.2(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P.
Nash (Ed.), ASM International,
Materials Park, OH, 1991).
Chapter 9- 6
PHASE DIAGRAMS: composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
• Examples:
Cu-Ni
system
Adapted from Fig. 9.2(b), Callister 6e.
(Fig. 9.2(b) is adapted from Phase Diagrams
of Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
Chapter 9- 7
PHASE DIAGRAMS: weight fractions of phases
• Rule 3: If we know T and Co, then we know:
--the amount of each phase (given in wt%).
• Examples:
Cu-Ni
system
S
43  35
 73wt %
WL   
R S 43  32
R
Wa  
R S
= 27wt%
Adapted from Fig. 9.2(b), Callister 6e.
(Fig. 9.2(b) is adapted from Phase Diagrams
of Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
Chapter 9- 8
THE LEVER RULE: A PROOF
• Sum of weight fractions: WL  Wa  1
• Conservation of mass (Ni): Co  WL CL  WaCa
• Combine above equations:
• A geometric interpretation:
moment equilibrium:
WLR  WaS
1 Wa
solving gives Lever Rule
Chapter 9- 9
EX: COOLING IN A Cu-Ni BINARY
• Phase diagram:
Cu-Ni system.
Cu-Ni
system
• System is:
--binary
i.e., 2 components:
Cu and Ni.
--isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100wt% Ni.
• Consider
Co = 35wt%Ni.
Callister 6e.
Chapter 9- 10
CORED VS EQUILIBRIUM PHASES
• Ca changes as we solidify.
• Cu-Ni case: First a to solidify has Ca = 46wt%Ni.
Last a to solidify has Ca = 35wt%Ni.
• Fast rate of cooling:
Cored structure
• Slow rate of cooling:
Equilibrium structure
Chapter 9- 11
MECHANICAL PROPERTIES: Cu-Ni System
• Effect of solid solution strengthening
on:
--Tensile strength (TS)
Adapted from Fig. 9.5(a), Callister 6e.
--Peak as a function of Co
--Ductility (%EL,%AR)
Adapted from Fig. 9.5(b), Callister 6e.
--Min. as a function of Co
Chapter 9- 12
BINARY-EUTECTIC SYSTEMS
2 components
has a special composition
with a min. melting T.
Cu-Ag
system
from Binary Phase Diagrams, 2nd ed., Vol. 1, T.B.
Massalski (Editor-in-Chief), ASM International,
Materials Park, OH, 1990.)
Chapter 9- 13
EX: Pb-Sn EUTECTIC SYSTEM (1)
• For a 40wt%Sn-60wt%Pb alloy at 150C, find...
--the phases present:
a+b
--the compositions of
the phases:
Pb-Sn
system
from Binary Phase Diagrams, 2nd ed., Vol. 3, T.B.
Massalski (Editor-in-Chief), ASM International,
Materials Park, OH, 1990.)
Chapter 9- 14
EX: Pb-Sn EUTECTIC SYSTEM (2)
• For a 40wt%Sn-60wt%Pb alloy at 150C, find...
--the phases present: a + b
--the compositions of
the phases:
Ca = 11wt%Sn
Cb = 99wt%Sn
--the relative amounts
of each phase:
Pb-Sn
system
from Binary Phase Diagrams, 2nd ed., Vol. 3, T.B.
Massalski (Editor-in-Chief), ASM International,
Materials Park, OH, 1990.)
Chapter 9- 15
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-I
• Co &lt; 2wt%Sn
• Result:
--polycrystal of a grains.
Callister 6e.
Chapter 9- 16
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-II
• 2wt%Sn &lt; Co &lt; 18.3wt%Sn
• Result:
--a polycrystal with fine
b crystals.
Pb-Sn
system
Callister 6e.
Chapter 9- 17
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-III
• Co = CE
• Result: Eutectic microstructure
--alternating layers of a and b crystals.
Pb-Sn
system
Adapted from Fig. 9.12, Callister 6e.
(Fig. 9.12 from Metals Handbook, Vol.
9, 9th ed., Metallography and
Microstructures, American Society
for Metals, Materials Park, OH, 1985.)
Callister 6e.
Chapter 9- 18
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-IV
• 18.3wt%Sn &lt; Co &lt; 61.9wt%Sn
• Result: a crystals and a eutectic microstructure
Pb-Sn
system
Callister 6e.
Chapter 9- 19
HYPOEUTECTIC &amp; HYPEREUTECTIC
Callister 6e. (Fig. 9.7
Phase Diagrams, 2nd
ed., Vol. 3, T.B. Massalski
(Editor-in-Chief), ASM
International, Materials
Park, OH, 1990.)
(Figs. 9.12 and
9.15 from Metals
Handbook, 9th ed.,
Vol. 9,
Metallography and
Microstructures,
American Society
for Metals,
Materials Park,
OH, 1985.)
Fig. 9.15, Callister 6e.
Callister 6e.
Callister 6e. (Illustration
only)
Chapter 9- 20
IRON-CARBON (Fe-C) PHASE DIAGRAM
(Adapted from Fig. 9.24, Callister 6e.
(Fig. 9.24 from Metals Handbook, 9th ed.,
Vol. 9, Metallography and
Microstructures, American Society for
Metals, Materials Park, OH, 1985.)
Adapted from Fig. 9.21,Callister 6e. (Fig. 9.21
adapted from Binary Alloy Phase Diagrams, 2nd ed.,
Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM
International, Materials Park, OH, 1990.)
Chapter 9- 21
HYPOEUTECTOID STEEL
9.21 and 9.26,Callister
from Binary Alloy
Phase Diagrams, 2nd
ed., Vol. 1, T.B.
Massalski (Ed.-inChief), ASM
International, Materials
Park, OH, 1990.)
Fig. 9.27,Callister
6e. (Fig. 9.27 courtesy Republic Steel Corporation.)
Chapter 9- 22
HYPEREUTECTOID STEEL
9.21 and 9.29,Callister
from Binary Alloy
Phase Diagrams, 2nd
ed., Vol. 1, T.B.
Massalski (Ed.-inChief), ASM
International, Materials
Park, OH, 1990.)
Fig. 9.30,Callister
6e. (Fig. 9.30
copyright 1971 by United States Steel Corporation.)
Chapter 9- 23
ALLOYING STEEL WITH MORE ELEMENTS
• Teutectoid changes:
Adapted from Fig. 9.31,Callister 6e. (Fig. 9.31
from Edgar C. Bain, Functions of the Alloying
Elements in Steel, American Society for
Metals, 1939, p. 127.)
• Ceutectoid changes:
Adapted from Fig. 9.32,Callister 6e. (Fig. 9.32
from Edgar C. Bain, Functions of the Alloying
Elements in Steel, American Society for
Metals, 1939, p. 127.)
Chapter 9- 24
SUMMARY
• Phase diagrams are useful tools to determine:
--the number and types of phases,
--the wt% of each phase,
--and the composition of each phase
for a given T and composition of the system.
• Alloying to produce a solid solution usually
--increases the tensile strength (TS)
--decreases the ductility.
• Binary eutectics and binary eutectoids allow for
a range of microstructures.
Chapter 9- 25
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